BrowserUk operates in an environment in which it is vital to squeeze every last, living computron from any processor, algorithm or function with which he deals, so I am not inclined to dispute his assertion that indirect access is "vastly less efficient".

The "vastly less efficient" was in response *only* to 7stud's suggested: my @ydata = @{shift()};.

Duplicating multiple, multi-dimensional arrays (in the case of mat mult), in order to achieve the same, non-indirected notation as you get with aliasing is "vastly less efficient".

Taking that quote, out of that context, is a strawman.

I would say that the (untested) way I have re-written mmMxM() below is, to my taste, at least as clear as the original.

For this simple example, it's not horribly more complex I grant you. But that is the tip of the iceberg.

Rather than this hard-coded sized, square-matrix multiply, let's take the more general form of MxN MatMult:

sub mmMxN {
    our( @M, @N );
    local( *M, *N ) = @_;
    die "Incompatible matrix dimensions" unless @M == @{ $N[0] };

    my @C = map[ (0) x @M ], 0 .. $#{ $N[ 0 ] };

    for my $i ( 0 .. $#M ) {
        for my $j ( 0 .. $#{ $N[0] } ) {
            $C[ $i ][ $j ] += $M[ $i ][ $_ ] * $N[ $_ ][ $j]  for 0 ..
+ $#N;
        }
    }
    return \@C;
}
[download]

Now the indirect notation would take a somewhat higher cost on clarity.

Now consider that this is a method within an OO module, and the matrices in question are named instance variables in the object:

sub mmMxN {
    my $self = shift;
    die "Incompatible matrix dimensions" unless @{ $self->{M} } == @{ 
+$self->{N}->[0] };

    $self->{R} = map[ (0) x @{ $self->{M} } ], 0 .. $#{ $self->{N}->[ 
+0 ] };

    for my $i ( 0 .. $#{ $self->{M} } ) {
        for my $j ( 0 .. $#{ $self->{N}->[0] } ) {
            $self->{R}->[$i]->[$j] += $self->{M}->[$i]->[$_] * $self->
+{N}->[$_]->[$j] for 0 .. $#{ $self->{N} };
        }
    }
    return $self->{R};
}
[download]

Yes, you can use temporaries for the array refs; and I've also exaggerated the syntax problem for effect, but even without that, this is preferable:

sub mmMxN {
    our ( @M, @N );
    my $self = shift;
    local( *M, *N ) = @{ $self }{ M, N };
    die "Incompatible matrix dimensions" unless @{ $M } == @{ $N[0] };

    my @R = map[ (0) x @M ], 0 .. $#N[ 0 ];

    for my $i ( 0 .. $#M ) {
        for my $j ( 0 .. $#{ $N[0] } ) {
            $R[$i][$j] += $M[$i][$_] * $N[$_][$j] for 0 .. $#N;
        }
    }
    $self->{R} = \@R;
}
[download]

(IMO anyway :)

PS. See also The seven good uses for local.